Question 957304
Find three integer or decimal solutions to the following equation, then graph the solution set. 
to do so, you need to choose three values for {{{x}}} and calculate {{{y}}} to find points that lie on this line, plot points and draw a line through

{{{4x-5y=20}}}....first solve for {{{y}}}
{{{4x-20=5y}}}
{{{4x/5-20/5=y}}}
{{{y=(4/5)x-4}}}
 
now we can choose ANY number for {{{x}}}: I would like {{{0}}},{{{5}}},and {{{-5}}}

{{{y=(4/5)x-4}}} if {{{x=0}}}

{{{y=(4/5)0-4}}}

{{{y=-4}}} 

so, first point is ({{{0}}},{{{-4}}}) which is y-intercept

{{{y=(4/5)x-4}}} if {{{x=5}}}

{{{y=(4/5)5-4}}}

{{{y=(4/cross(5))cross(5)-4}}}

{{{y=4-4}}} 

{{{y=0}}}
 
second point is ({{{5}}},{{{0}}}) which is x-intercept


{{{y=(4/5)x-4}}} if {{{x=-5}}}

{{{y=(4/5)(-5)-4}}}

{{{y=(4/cross(5))cross(5)-4}}}

{{{y=-4-4}}} 

{{{y=-8}}}
 
second point is ({{{-5}}},{{{-8}}})

now we can plot points:

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-5,-8,.12),circle(5,0,.12),circle(0,-4,.12),
locate(-5,-8,p(-5,-8)),locate(5,0.5,p(5,0)),locate(0,-4,p(0,-4)),
 graph( 600, 600, -10, 10, -10, 10, 0)) }}} 

then draw a line:

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-5,-8,.12),circle(5,0,.12),circle(0,-4,.12),
locate(-5,-8,p(-5,-8)),locate(5,0.5,p(5,0)),locate(0,-4,p(0,-4)),
 graph( 600, 600, -10, 10, -10, 10, (4/5)x-4)) }}} 



if requesting ({{{104}}}, {{{105}}}), ({{{101}}}, {{{96}}}), ({{{200}}}, {{{300}}}) then I can check if these points lie on given line

{{{y=(4/5)x-4}}} if {{{x=104}}}

{{{y=(4/5)104-4}}}
{{{y=416/5-4}}}

{{{y=79.2}}}....so, ({{{104}}}, {{{105}}}) is {{{not}}} solution for given equation

check it ones again with {{{4x-20=5y}}}

{{{4*104-20=5*105}}}
{{{416-20=525}}}
{{{396<>525}}}

check second point ({{{101}}}, {{{96}}})
{{{4*101-20=5*96}}}
{{{404-20=480}}}
{{{384<>480}}}

and third point ({{{200}}}, {{{300}}})

{{{4*200-20=5*300}}}
{{{800-20=1500}}}
{{{780<>1500}}}

so, these points do NOT lie on a line {{{4x-20=5y}}}

see it on a graph:

{{{drawing( 600, 600, -40, 400, -40, 400,
circle(200,300,1.3),circle(101,96,1.3),circle(104,105,1.3),
locate(200,300,p(200,300)),locate(101,96.5,p(101,96)),locate(104,105,p(104,105)),
 graph( 600, 600, -40, 400, -40, 400, (4/5)x-4)) }}}